I think the bubonic plague connection was one I picked up at the British Museum during my first visit to London. I thought it was really cool that something so devastating would have such a silver lining... I'm guessing that fewer people died in the fires/cold (I didn't see numbers there) than had been dying from plague.
I had to look up that Act. Wasn't given royal assent until the following Feb, but it sounds rather modern that they used the cover of societal panic to do some shady work.
The Great Fire of London was out by the 6th of September... and would have threatened the Buildings of Parliament anyway, probably putting whatever they were writing on hold - that fire didn't choose to exclude the homes of the famous, such as Samuel Pepys. It only stopped at the Thames shore - and only because London Bridge had suffered a major fire a couple of decades before - and hadn't been reconstructed. So, South of the Thames was spared the flames, but perhaps not the Plague... I didn't look into that aspect either.